The solution to the initial-value problem is: y(x) = (1/2) x ln(x) + (1/4) x
To solve this initial-value problem, we will use the method of undetermined coefficients.
First, we assume that the solution has the form:
y(x) = axln(x) + bx + c
where a, b, and c are constants to be determined. We differentiate this equation twice to obtain:
y'(x) = a(ln(x) + 1) + b
y''(x) = a/x
Substituting these expressions into the differential equation, we get:
x(a/x) - 2x(a(ln(x) + 1) + b) + 2(axln(x) + bx + c) = x ln(x)
Simplifying this equation, we get:
(a - 2b + 2c) xln(x) + (-2a + 2b) x + 2c = x ln(x)
Equating the coefficients of x ln(x), x, and the constant term, we get the following system of equations:
a - 2b + 2c = 1
-2a + 2b = 0
2c = 0
Solving for a, b, and c, we get:
a = 1/2
b = 1/4
c = 0
Therefore, the solution to the initial-value problem is:
y(x) = (1/2) x ln(x) + (1/4) x + 0
To verify that this solution satisfies the differential equation and the initial conditions, we differentiate y(x) and substitute it into the differential equation:
y'(x) = (1/2) ln(x) + (1/4)
y''(x) = 1/(2x)
xy''(x) - 2xy'(x) + 2y(x) = x ln(x)
So the differential equation is satisfied. Finally, we substitute x = 1 into y(x) and y'(x) to get:
y(1) = (1/2) + (1/4) + 0 = 3/4
y'(1) = (1/2)(0) + (1/4) = 1/4
Therefore, the solution to the initial-value problem is:
y(x) = (1/2) x ln(x) + (1/4) x
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HELP ASAP!!!!!!!!
Find the cite of each variabile
tan = opp/adj
x = 13(tan 45)
x = 13
//
a² + b² = c²
13² + 13² = 338²
square root of 338 is not a rational number so turn into mixed radical.
//
[tex]x \: = 13[/tex]
[tex]y = 13 \sqrt{2} [/tex]
HELP! WILL GIVE BRAINLY!!! Find the volume of a cylinder with height = 10ft and the diameter of the base circle is 12ft.
Answer:
About 1,130.4 Cubic Feet
(My previous answer was a mistake. It has now been corrected)
Step-by-step explanation:
The Volume of a cylinder = Height * Pi * Radius^2
The radius is half the diameter, so 12 ÷ 2 = 6
Pi rounded to the hundredth place is 3.14.
Volume = 10 * 3.14 * 6^2 = 1,130.4
Therefore the Volume is about 1,130.4 cubic feet.
Answer:
Exact Volume = 360pi cubic feet
Approximate Volume = 1130.4 cubic feet
The approximate volume is found when you use pi = 3.14; use more decimal digits of pi to get a more accurate value.
===========================================================
Explanation:
The volume of a cylinder is found by the formula
V = pi*r^2*h
where,
pi = 3.14 approximatelyr = radius = 6 ft, since the radius is half the diameter.h = height = 10 ftSo,
V = pi*r^2*h
V = pi*6^2*10
V = pi*36*10
V = pi*360
V = 360pi ........... exact volume in terms of pi
V = 360*3.14
V = 1130.4 ......... approximate volume if you use pi = 3.14
The units of the volume are in "cubic feet" which we can abbreviate to "ft^3". Think of a 1 ft by 1 ft by 1 ft cube. The volume would be 1*1*1 = 1 cubic foot. So basically having a volume of roughly 1130 cubic feet means we need this many cubic blocks to form the cylinder (some of the blocks will be cut up to be able to fit).
If there was a point R(-2, 4) and it was dilated to R'(-8, 16), what was the scale factor? *
Answer:
4
Step-by-step explanation:
1. 12x – 8x + 4 = 20
2. 9w + 4w – 5w + w = -9
Answer:
the answer for just eliminate the variables and to the solving tho get the answer as they get the answer to the number above
What is the measure of arc FG?
PLEASE HELP , i’ll make BRAINLIEST
Question: 1 out of 10
~!¡! Volume !¡!~
Answer:
a) 96
Step-by-step explanation:
2 + 2 = 4
4 * 24 = 96
Justin wants to place one of his 4 signed hockey sticks on his shelf. The length of the shelf is exactly 1.05 meters. His 4 hockey sticks and their lengths are shown below.
Answer:
Stick 2
Step-by-step explanation:
Given
[tex]L = 1.05m[/tex] --- Shelf length
Missing information from the question are:
[tex]Stick\ 1 = 1.4m[/tex]
[tex]Stick\ 2 = 1.041m[/tex]
[tex]Stick\ 3 = 1.14m[/tex]
[tex]Stick\ 4 = 1.104m[/tex]
See attachment
Required
Which stick best fits the shelf?
The following observations are to be noted:
The length of stick 1 of 1.4m is greater than the length of the shelfThe length of stick 3 of 1.14m is greater than the length of the shelfThe length of stick 4 of 1.104m is greater than the length of the shelfOnly stick 2 (of length 1.041m) has a smaller length when compared to the length of the shelf.
Hence, Justin should choose stick 2
Amelia bought 40 plain black T-shirts for $4 each.She painted designs on them and then sold each T-shirt for 7.50.How much profit did Amelia make selling her fancy T-shirts?
I hope this helpfull dor you...But if this not helpfull,im so sorry...
Evaluate the expression when a=−15 and b=−5.
hat would -
A divided by b = ?
be?
Answer:
3Step-by-step explanation:
Given the following values a=−15 and b=−5.
We are to find a/b
a/b = -15/-5
a/b = 15/3
a/b = 5*3/5*1
a/b = 5/5 * 3
a/b = 1*3
a/b = 3
Hence a divided b will be 3
3.3 - 3.7n - 2n + 8 nnnnnnnnnnnnnnnnnn
Answer:
-5.7n + 11.3
Step-by-step explanation:
3.3 - 3.7n - 2n + 8 = -3.7n - 2n + 3.3 + 8 = -5.7n + 11.3
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Can you please help because I’m stuck
Answer:
2x+7= 3x-10
17=x
Step-by-step explanation:
Find the value of x in the triangle, pls help I need this so bad, if you want points you can tell me in the COMMENTS and I'll make a thing just for u!! But pls don't answer if u don't know♥️ thanks love u!!
Answer:
67 degrees, the 4th choice.
Step-by-step explanation:
As you may know, sum of angles in a triangle is 180 degrees. The best thing about this question here, is that 2 of the angles are already given. Now, all you need to do is add the two angles and subtract the result from 180.
You can also use the process of elimination to start.
First off, you can eliminate the second answer, sum of angles in triangle is 180, and 293 is way to much.
7 degrees is way too little, and it can be found by common sense, and knowing that 7+60+53 is already gonna be less than 180. (Didnt mean to be rude though. lol)
The only options left are 113 degrees and 67 degrees. now, lets use the actual formula of sum of angles in triangle.
60+53=113
180-113=67.
So, its 67 degrees! Process of elimination can help, but if you need proof for your answer, do not do that work in front of your teachers, only show the actual proof.
Hope you learned and liked my explanation! If so, please leave a rating and thanks (and hopefully brainliest!!) Have a great day!
I am in need of help
Answer:
The answer is Step 2: m<w + m<z = 180 degrees (suppplmentary angles).
Step-by-step explanation:
First, Step 2 says m<w - m<z = 90 degrees. That's false because the m<w - m<z would equal an acute angle, not a right angle. Secondly, the m<w + m<z = 180 degrees. Supplementary angles equal 180 degrees.
3) If the slope of PQ is 4 and the slope of OR is – 1/2 , find the slope of SR so that PQRS is a parallelogram.
Answer:
Step-by-step explanation:
the anwser is 1/3
how do you work out this problem?
Answer:
7 meters long
Step-by-step explanation:
Part A: find the value for x:
Part B: what is the value of angle A?
Answer:
part A:
If ABC is a triangle then,
2x+4+2x-9+x=180degree
or, 5x-5=180degree
or, 5x=(180+5)degree
or, 5x= 185degree
or, x=185÷5 = 37degree ans.
PartB
now put the value of x in angle A
i.e angle A = 2x-9
or, angle A= (2×37) - 9
or, angle A= 74 - 9
therefore, angle A= 65degree ans.
Please I need this TOMORROW
Answer:
here u go !! <3
Part 1:
1. 18 - [(15 - 9 + 4] - 2 = 6
2. 6² - [3² + (3 + 12)] = 12
3. 21 - [(2 × 4) + 2 + 5] = 6
4. [(17 - 10) + 4] + 5² = 36
5. 36 ÷ 6 + [(5 × 3) + (13 - 6) + 10] = 38
Part 2:
6. 15 ÷ 3 × 5 - 16 = c. 9
7. 2 [5 + (30 ÷ 6)²] = d. 60
8. [3² × 4] - [6 + 4²] = b. 14
9. 8 [6² - 3 × (2 + 5) - 8 + 3] = e. 80
10. 15 - {27 - 2 × [33 - 4 × (5 + 1)]} = a. 6
Answer:
(1 )14
(2) 45
(3) 20
(4) 36
(5)121
(6) 6
(7)9
(8) 14
(9)80
(10)60
Write an equivalent expression by distributing the "
−−" sign outside the parentheses:
−(3h−2.3k)−7
Answer:
= -3h + 2.3k -7
Step-by-step explanation:
you want to distribute your negative to each value in parentheses
remember that negative x negative = positive
remember that negative x positive = negative
please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!will give brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
vertical angles
Step-by-step explanation:
They don't share a common side, so they are not adjacent!
Hope that helps!
3. Plot the points and then answer the questions:
(1, -3) (-3, 9) (2,-6)
a. Is this a proportional relationship?
b. What is the constant of proportionality?
Please help !!
Answer:
a. yes there is a proportional relationship
b. I believe the constant is -3
If the area of the rectangle to be drawn is 20 square units, where should points B and D be located if they lie to the right of points A and C?
The question is incomplete. Here is the complete question.
If the area of the rectangle to be drawn is 20 square units, where should points B and D be located if they lie to the right of points A and C?
B(1, 3) and D(1, −2)
B(3, 3) and D(3, −2)
B(2, 3) and D(2, −2)
B(1, 2) and D(1, −3)
Answer: B(1, 3) and D(1, -2)
Step-by-step explanation: Area of a rectangle is the multiplication of its width and its length.
The rectangle to be has length, or distance from point A to point C, of 5 units.
For the area to be 20, width has to be 4.
Point B will be 4 units to the right of point A, which means:
[tex]x_{B}=x_{A}+4[/tex]
Point A has coordinates ( -3, 3), then:
[tex]x_{B}=-3+4[/tex]
[tex]x_{B}=1[/tex]
Because the points is "moved" to the right, instead of up or down, y-coordinate stays the same:
[tex]y_{B}=y_{A}[/tex]
[tex]y_{B}=3[/tex]
Point D will be 4 units to the right of point C:
[tex]x_{D}=x_{C}+4[/tex]
Coordinates of point C are ( -3, -2):
[tex]x_{D}=-3+4[/tex]
[tex]x_{D}=1[/tex]
Because a rectangle has a pair of sides parallel to each other, D's y-coordinate will also be the same:
[tex]y_{D}=y_{C}[/tex]
[tex]y_{D}=-2[/tex]
Coordinates of points B and D that makes rectangle ABCD have area of 20 square units are (1, 3) and (1, -2), respectively.
Claire borrows money from a bank. She has to pay a $50 fee for borrowing money and $0.55 every day until the money is paid back. Which function below represents this situation?
A f(x) = 50 +0.55x
B f(x) = 50x +0.55
C f(x) = 55 +0.50x
D f(x) = 55x +0.50
Answer:
The correct answer is A)
Step-by-step explanation:
A seabird is 28 meters above the surface of the ocean. What is its elevation?
Answer:
The elevation is 28 meters.
Step-by-step explanation:
This is pretty obvious because it says that the bird is above the ocean, not below. So, it is positive.
Hope this helps! :)
The temperature outside changed from 64°F to 43°F over a period of seven days. If the temperature changed by the same amount each day, what was the daily temperature change?
Answer: -3°F
Step-by-step explanation:
From the question, we are informed that the temperature outside changed from 64°F to 43°F over a period of seven days. The total change will be:
= 43°F - 64°F
= -21°F
If the temperature changed by the same amount each day, the daily temperature change will now be:
= -21°F / 7
= -3°F
The temperature decreased by 3°F daily
How do I know if it is sss, sad, asa, or aas?
i have attached a image which may help u <3
Work out, giving your answer in its simplest form:
3 1/2 divided by 2 3/5
1 9/26
Convert any mixed numbers to fractions.
Then your initial equation becomes:
7/2÷13/5
Applying the fractions formula for division,=7×5
2×13
=35/26
Simplifying 35/26, the answer is...35/26=1 9/26
Answer:
1 [tex]\frac{9}{26}[/tex]
Step-by-step explanation:
Given
3 [tex]\frac{1}{2}[/tex] ÷ 2 [tex]\frac{3}{5}[/tex] ← change mixed numbers to improper fractions
= [tex]\frac{7}{2}[/tex] ÷ [tex]\frac{13}{5}[/tex]
To perform the division
Leave the first fraction, change division to multiplication and turn the second fraction upside down.
= [tex]\frac{7}{2}[/tex] × [tex]\frac{5}{13}[/tex] ← multiply numerators/ denominators together
= [tex]\frac{35}{26}[/tex]
= 1 [tex]\frac{9}{26}[/tex]
-8a^2+40a=
this is a factoring question
Answer:
-8a(a-5)
Step-by-step explanation:
-8a^2+40a
-8a(a-5)
In an isosceles trapezoid the base angles are?
Answer:
The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary angle of a base angle at the other base
Step-by-step explanation:
Test Scores. You are taking a math test in which items in part A are worth 10 points and items in part B are worth 15 points. It takes 3 min. to complete each item of part A and 6 min. to complete each item in part B. The total time allowed is 60 min. and you do exactly 16 questions. How many questions of each part did you complete? Assuming that all your answers were correct, after all you had a GREAT Math Teacher, what was your score?
Answer:
465 is the total points he got and he solved 14 in part A and 2 in part B
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Parallel or perpendicular